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<div class="title">EquationBlocks.cs</div>  </div>
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<div class="contents">
<a href="_equation_blocks_8cs.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">using</span> System;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">using</span> System.Collections.Generic;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="keyword">using</span> System.Linq;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="keyword">using</span> System.Text;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">using</span> SystemSharp.Algebraic;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="keyword">using</span> SystemSharp.SysDOM;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="keyword">using</span> SystemSharp.Meta;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="keyword">using</span> GraphAlgorithms;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;</div>
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="namespace_system_sharp_1_1_algebraic.html">   29</a></span>&#160;<span class="keyword">namespace </span>SystemSharp.<a class="code" href="namespace_system_sharp_1_1_sys_d_o_m.html#af42b902eef7452e162a95b646eeea911ab4777b408acf603e260974d5d8e9e930">Algebraic</a></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;{</div>
<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">   31</a></span>&#160;    <span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">EquationSystem</a></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    {</div>
<div class="line"><a name="l00033"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a8659758da44e3ab893d912b80ad649cf">   33</a></span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a8659758da44e3ab893d912b80ad649cf">EquationSystem</a>()</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        {</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;            Variables = <span class="keyword">new</span> List&lt;Variable&gt;();</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;            Equations = <span class="keyword">new</span> List&lt;Expression&gt;();</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        }</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a7394da852fbcc1fb008e8221afef37ff">   39</a></span>&#160;        <span class="keyword">public</span> List&lt;Variable&gt; Variables { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#aed8bb66c45e4450aa85d310bedde5240">   40</a></span>&#160;        <span class="keyword">public</span> List&lt;Expression&gt; Equations { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keyword">private</span> <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_matrix.html">Matrix</a> _jac;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        <span class="keyword">private</span> <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a>[] _residual;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_matrix.html">Matrix</a> Jacobian</div>
<div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#ad619f8828864b2e40c9a1008d7e8cc2a">   46</a></span>&#160;        {</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            <span class="keyword">get</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            {</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;                <span class="keywordflow">if</span> (_jac == null)</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                {</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;                    <a class="code" href="class_system_sharp_1_1_meta_1_1_type_descriptor.html">TypeDescriptor</a> type;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;                    <span class="keywordflow">foreach</span> (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a> eq <span class="keywordflow">in</span> Equations)</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;                        type = eq.ResultType;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;                    _jac = <span class="keyword">new</span> <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_matrix.html">Matrix</a>(Equations.Count, Variables.Count);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; Equations.Count; i++)</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;                    {</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; Variables.Count; j++)</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;                        {</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;                            _jac[i, j] = Equations[i].Derive(Variables[j]).Simplify();</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                            type = _jac[i,j].ResultType;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;                        }</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;                    }</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;                }</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;                <span class="keywordflow">return</span> _jac;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            }</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        }</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="keyword">public</span> <span class="keywordtype">bool</span> IsLinear</div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#aa4ae75591ac16ae17346f4bed103f1d3">   70</a></span>&#160;        {</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            <span class="keyword">get</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            {</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;                IEnumerable&lt;LiteralReference&gt; lrs =</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;                    from <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_variable.html">Variable</a> v in Variables</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                    select (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference.html">LiteralReference</a>)v;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_matrix.html">Matrix</a> jac = Jacobian;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; jac.NumRows; i++)</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;                {</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;                    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; jac.NumCols; j++)</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                    {</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                        <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a> e = jac[i, j];</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;                        <span class="keywordflow">if</span> (e.ExtractLiteralReferences().Intersect(lrs).Count() &gt; 0)</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;                            <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;                    }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;                }</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;            }</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        }</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a>[] Residual</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a72da8aac367e62a7786ed7038e6866f6">   92</a></span>&#160;        {</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;            <span class="keyword">get</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;            {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;                <span class="keywordflow">if</span> (_residual == null)</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;                {</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;                    _residual = <span class="keyword">new</span> <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a>[Equations.Count];</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; _residual.Length; i++)</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                        _residual[i] = Equations[i];</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; Variables.Count; j++)</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                    {</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                        <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_variable.html">Variable</a> v = Variables[j];</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                        <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a> ve = (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a>)v;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                        <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; _residual.Length; i++)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                        {</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;                            _residual[i] = _residual[i].Substitute(ve, SpecialConstant.ScalarZero);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                        }</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                    }</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                }</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                <span class="keywordflow">return</span> _residual;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;            }</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        }</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;</div>
<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#ad36576a8e21b2006beedb4a3d8e65bd7">  115</a></span>&#160;        <span class="keyword">public</span> <span class="keywordtype">void</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#ad36576a8e21b2006beedb4a3d8e65bd7">CheckConsistency</a>()</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        {</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;            <span class="keywordflow">foreach</span> (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a> e <span class="keywordflow">in</span> Equations)</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                e.CheckConsistency();</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        }</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    }</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;</div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">  122</a></span>&#160;    <span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    {</div>
<div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html#ace090b625a7246219e48de2b2bd6c206">  124</a></span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html#ace090b625a7246219e48de2b2bd6c206">EquationBlock</a>()</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;            EqSys = <span class="keyword">new</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">EquationSystem</a>();</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;            Successors = <span class="keyword">new</span> List&lt;EquationBlock&gt;();</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;            Predecessors = <span class="keyword">new</span> List&lt;EquationBlock&gt;();</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        }</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;</div>
<div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html#abe0afa336b753203e06461539d9ff815">  131</a></span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">EquationSystem</a> EqSys { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html#a70a1a032f56a78c65903a3ec803f3f90">  132</a></span>&#160;        <span class="keyword">public</span> List&lt;EquationBlock&gt; Successors { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00133"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html#a1e38989d323248eb359dbb13b28b7dcd">  133</a></span>&#160;        <span class="keyword">public</span> List&lt;EquationBlock&gt; Predecessors { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;</div>
<div class="line"><a name="l00136"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html">  136</a></span>&#160;    <span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html">EquationDecomposition</a></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    {</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;        <span class="keyword">private</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html">EquationDecomposition</a>(<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">EquationSystem</a> eqsys)</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        {</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;            <span class="keywordflow">if</span> (eqsys == null ||</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;                eqsys.<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#aed8bb66c45e4450aa85d310bedde5240">Equations</a> == null ||</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;                eqsys.<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a7394da852fbcc1fb008e8221afef37ff">Variables</a> == null)</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;                <span class="keywordflow">throw</span> <span class="keyword">new</span> ArgumentException(<span class="stringliteral">&quot;null reference in equation system argument&quot;</span>);</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;            <span class="keywordflow">if</span> (eqsys.<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#aed8bb66c45e4450aa85d310bedde5240">Equations</a>.Count != eqsys.<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a7394da852fbcc1fb008e8221afef37ff">Variables</a>.Count)</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;                <span class="keywordflow">throw</span> <span class="keyword">new</span> ArgumentException(<span class="stringliteral">&quot;equation system is not well-constrained!&quot;</span>);</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            <span class="keywordtype">int</span> curidx = 0;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;            <span class="keywordflow">foreach</span> (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a> eq <span class="keywordflow">in</span> eqsys.<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#aed8bb66c45e4450aa85d310bedde5240">Equations</a>)</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;            {</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;                eq.Cookie = curidx++;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;            }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;            Dictionary&lt;object, int&gt; idx = <span class="keyword">new</span> Dictionary&lt;object, int&gt;();</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;            <span class="keywordflow">foreach</span> (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_variable.html">Variable</a> v <span class="keywordflow">in</span> eqsys.<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a7394da852fbcc1fb008e8221afef37ff">Variables</a>)</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;            {</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                idx[v] = curidx++;</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;            }</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;            <span class="comment">// Steps 1 and 2: Construct G and Gd</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;            <a class="code" href="class_graph_algorithms_1_1_graph.html">Graph</a> g = <span class="keyword">new</span> <a class="code" href="class_graph_algorithms_1_1_graph.html">Graph</a>(curidx);</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;            <a class="code" href="class_graph_algorithms_1_1_digraph.html">Digraph</a> dg = <span class="keyword">new</span> <a class="code" href="class_graph_algorithms_1_1_digraph.html">Digraph</a>(curidx);</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; eqsys.Equations.Count; i++)</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;            {</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;                <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">Expression</a> eq = eqsys.Equations[i];</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;                <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference.html">LiteralReference</a>[] lrs = eq.ExtractLiteralReferences();</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;                <span class="keywordflow">foreach</span> (<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference.html">LiteralReference</a> lr <span class="keywordflow">in</span> lrs)</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;                {</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                    <span class="keywordtype">int</span> j;</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                    <span class="keywordflow">if</span> (idx.TryGetValue(lr.<a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference.html#a85c86e184c594f162c9a1ca3881098c7">ReferencedObject</a>, out j))</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;                    {</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;                        g.AddEdge(i, j);</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;                        dg.AddEdge(i, j);</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                    }</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;                }</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;            }</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;            <span class="comment">// Step 1: Maximum matching</span></div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;            <a class="code" href="class_graph_algorithms_1_1_matching.html">GraphAlgorithms.Matching</a> m = g.GetMaximumMatching();</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;            <span class="keywordtype">bool</span> success = m.IsMaximumCardinality;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; eqsys.Equations.Count; i++)</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;            {</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;                <span class="keywordtype">int</span> k = m[i];</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;                <span class="keywordflow">if</span> (k &gt;= 0)</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;                    dg.AddEdge(k, i);</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;            }</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;            <span class="comment">// Step 2: Strongly connected components</span></div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;            <a class="code" href="class_graph_algorithms_1_1_strong_components.html">StrongComponents</a> sc = dg.GetStrongComponents();</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;            <span class="keywordtype">int</span> numc = sc.NumComponents;</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;            <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a>[] blocks = <span class="keyword">new</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a>[numc];</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numc; i++)</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;            {</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;                blocks[i] = <span class="keyword">new</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a>();</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;            }</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;            <span class="comment">// Step 3: Construct the tree</span></div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;            <a class="code" href="class_graph_algorithms_1_1_digraph.html">Digraph</a> dg2 = <span class="keyword">new</span> <a class="code" href="class_graph_algorithms_1_1_digraph.html">Digraph</a>(numc);</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; eqsys.Equations.Count; i++)</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;            {</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;                <span class="keywordtype">int</span> c = sc[i];</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;                blocks[c].EqSys.Equations.Add(eqsys.Equations[i]);</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;                <span class="keywordtype">int</span> vi = m[i];</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;                <a class="code" href="class_system_sharp_1_1_sys_d_o_m_1_1_variable.html">Variable</a> v = eqsys.Variables[vi - eqsys.Equations.Count];</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;                blocks[c].EqSys.Variables.Add(v);</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;                List&lt;int&gt; outset = dg.GetOutSet(i);</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;                <span class="keywordflow">foreach</span> (<span class="keywordtype">int</span> ovi <span class="keywordflow">in</span> outset)</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;                {</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;                    <span class="keywordtype">int</span> oc = sc[ovi];</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;                    <span class="keywordflow">if</span> (c != oc)</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;                        dg2.AddEdge(c, oc);</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;                }</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            }</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;            List&lt;int&gt; rootSet = <span class="keyword">new</span> List&lt;int&gt;();</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;            List&lt;int&gt; sinkSet = <span class="keyword">new</span> List&lt;int&gt;();</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> c = 0; c &lt; numc; c++)</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;            {</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;                <span class="keywordflow">if</span> (dg2.GetOutDegree(c) == 0)</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;                    rootSet.Add(c);</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;                <span class="keywordflow">if</span> (dg2.GetInDegree(c) == 0)</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;                    sinkSet.Add(c);</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;                List&lt;int&gt; outset = dg2.GetOutSet(c);</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;                <span class="keywordflow">foreach</span> (<span class="keywordtype">int</span> oc <span class="keywordflow">in</span> outset)</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;                    blocks[c].Predecessors.Add(blocks[oc]);</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;                List&lt;int&gt; inset = dg2.GetInSet(c);</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;                <span class="keywordflow">foreach</span> (<span class="keywordtype">int</span> ic <span class="keywordflow">in</span> inset)</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;                    blocks[c].Successors.Add(blocks[ic]);</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;            }</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;            RootSet = (from <span class="keywordtype">int</span> c in rootSet</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;                       select blocks[c]).ToArray();</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;            SinkSet = (from <span class="keywordtype">int</span> c in sinkSet</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;                       select blocks[c]).ToArray();</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;            AllBlocks = blocks;</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;        }</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;</div>
<div class="line"><a name="l00278"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html#adc59a1e12ea9cdca6efdb9ccf6551f84">  278</a></span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a>[] RootSet { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00279"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html#a6a21b9180923858f8c756e8a78f4d272">  279</a></span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a>[] SinkSet { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00280"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html#a49b87d25a730d865219a12facb3b2c5f">  280</a></span>&#160;        <span class="keyword">public</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">EquationBlock</a>[] AllBlocks { <span class="keyword">get</span>; <span class="keyword">private</span> set; }</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;</div>
<div class="line"><a name="l00282"></a><span class="lineno"><a class="line" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html#ab4981ea26957f2e0a7f3d4ae850f3c02">  282</a></span>&#160;        <span class="keyword">public</span> <span class="keyword">static</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html">EquationDecomposition</a> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html#ab4981ea26957f2e0a7f3d4ae850f3c02">Decompose</a>(<a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">EquationSystem</a> eqsys)</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;        {</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;            <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html">EquationDecomposition</a>(eqsys);</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        }</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    }</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;}</div>
<div class="ttc" id="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference_html_a85c86e184c594f162c9a1ca3881098c7"><div class="ttname"><a href="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference.html#a85c86e184c594f162c9a1ca3881098c7">SystemSharp.SysDOM.LiteralReference.ReferencedObject</a></div><div class="ttdeci">ILiteral ReferencedObject</div><div class="ttdoc">The reference literal </div><div class="ttdef"><b>Definition:</b> <a href="_core_algebraic_8cs_source.html#l02134">CoreAlgebraic.cs:2134</a></div></div>
<div class="ttc" id="class_graph_algorithms_1_1_matching_html"><div class="ttname"><a href="class_graph_algorithms_1_1_matching.html">GraphAlgorithms::Matching</a></div><div class="ttdef"><b>Definition:</b> <a href="_graph_algorithm_lib_8h_source.html#l00044">GraphAlgorithmLib.h:44</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_block_html"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_block.html">SystemSharp.Algebraic.EquationBlock</a></div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00122">EquationBlocks.cs:122</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_sys_d_o_m_1_1_expression_html"><div class="ttname"><a href="class_system_sharp_1_1_sys_d_o_m_1_1_expression.html">SystemSharp.SysDOM.Expression</a></div><div class="ttdoc">An expression. </div><div class="ttdef"><b>Definition:</b> <a href="_core_algebraic_8cs_source.html#l01096">CoreAlgebraic.cs:1096</a></div></div>
<div class="ttc" id="class_graph_algorithms_1_1_strong_components_html"><div class="ttname"><a href="class_graph_algorithms_1_1_strong_components.html">GraphAlgorithms::StrongComponents</a></div><div class="ttdef"><b>Definition:</b> <a href="_graph_algorithm_lib_8h_source.html#l00095">GraphAlgorithmLib.h:95</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_system_html_ad36576a8e21b2006beedb4a3d8e65bd7"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#ad36576a8e21b2006beedb4a3d8e65bd7">SystemSharp.Algebraic.EquationSystem.CheckConsistency</a></div><div class="ttdeci">void CheckConsistency()</div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00115">EquationBlocks.cs:115</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_decomposition_html_ab4981ea26957f2e0a7f3d4ae850f3c02"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html#ab4981ea26957f2e0a7f3d4ae850f3c02">SystemSharp.Algebraic.EquationDecomposition.Decompose</a></div><div class="ttdeci">static EquationDecomposition Decompose(EquationSystem eqsys)</div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00282">EquationBlocks.cs:282</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_sys_d_o_m_1_1_variable_html"><div class="ttname"><a href="class_system_sharp_1_1_sys_d_o_m_1_1_variable.html">SystemSharp.SysDOM.Variable</a></div><div class="ttdoc">A local variable. </div><div class="ttdef"><b>Definition:</b> <a href="_literals_8cs_source.html#l00195">Literals.cs:195</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_system_html_a8659758da44e3ab893d912b80ad649cf"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a8659758da44e3ab893d912b80ad649cf">SystemSharp.Algebraic.EquationSystem.EquationSystem</a></div><div class="ttdeci">EquationSystem()</div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00033">EquationBlocks.cs:33</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_decomposition_html"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_decomposition.html">SystemSharp.Algebraic.EquationDecomposition</a></div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00136">EquationBlocks.cs:136</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_system_html"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_system.html">SystemSharp.Algebraic.EquationSystem</a></div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00031">EquationBlocks.cs:31</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_system_html_aed8bb66c45e4450aa85d310bedde5240"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#aed8bb66c45e4450aa85d310bedde5240">SystemSharp.Algebraic.EquationSystem.Equations</a></div><div class="ttdeci">List&lt; Expression &gt; Equations</div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00040">EquationBlocks.cs:40</a></div></div>
<div class="ttc" id="class_graph_algorithms_1_1_digraph_html"><div class="ttname"><a href="class_graph_algorithms_1_1_digraph.html">GraphAlgorithms::Digraph</a></div><div class="ttdef"><b>Definition:</b> <a href="_graph_algorithm_lib_8h_source.html#l00236">GraphAlgorithmLib.h:236</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_sys_d_o_m_1_1_matrix_html"><div class="ttname"><a href="class_system_sharp_1_1_sys_d_o_m_1_1_matrix.html">SystemSharp.SysDOM.Matrix</a></div><div class="ttdoc">A matrix whose elements a expressions. </div><div class="ttdef"><b>Definition:</b> <a href="_core_algebraic_8cs_source.html#l03760">CoreAlgebraic.cs:3760</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_block_html_ace090b625a7246219e48de2b2bd6c206"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_block.html#ace090b625a7246219e48de2b2bd6c206">SystemSharp.Algebraic.EquationBlock.EquationBlock</a></div><div class="ttdeci">EquationBlock()</div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00124">EquationBlocks.cs:124</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_algebraic_1_1_equation_system_html_a7394da852fbcc1fb008e8221afef37ff"><div class="ttname"><a href="class_system_sharp_1_1_algebraic_1_1_equation_system.html#a7394da852fbcc1fb008e8221afef37ff">SystemSharp.Algebraic.EquationSystem.Variables</a></div><div class="ttdeci">List&lt; Variable &gt; Variables</div><div class="ttdef"><b>Definition:</b> <a href="_equation_blocks_8cs_source.html#l00039">EquationBlocks.cs:39</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_meta_1_1_type_descriptor_html"><div class="ttname"><a href="class_system_sharp_1_1_meta_1_1_type_descriptor.html">SystemSharp.Meta.TypeDescriptor</a></div><div class="ttdoc">Describes a type. </div><div class="ttdef"><b>Definition:</b> <a href="_type_descriptor_8cs_source.html#l00120">TypeDescriptor.cs:120</a></div></div>
<div class="ttc" id="class_graph_algorithms_1_1_graph_html"><div class="ttname"><a href="class_graph_algorithms_1_1_graph.html">GraphAlgorithms::Graph</a></div><div class="ttdoc">summary&gt;A directed graph. Vertices are represented by integer values.</div><div class="ttdef"><b>Definition:</b> <a href="_graph_algorithm_lib_8h_source.html#l00201">GraphAlgorithmLib.h:201</a></div></div>
<div class="ttc" id="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference_html"><div class="ttname"><a href="class_system_sharp_1_1_sys_d_o_m_1_1_literal_reference.html">SystemSharp.SysDOM.LiteralReference</a></div><div class="ttdoc">A reference expression to a literal. </div><div class="ttdef"><b>Definition:</b> <a href="_core_algebraic_8cs_source.html#l02101">CoreAlgebraic.cs:2101</a></div></div>
<div class="ttc" id="namespace_system_sharp_1_1_sys_d_o_m_html_af42b902eef7452e162a95b646eeea911ab4777b408acf603e260974d5d8e9e930"><div class="ttname"><a href="namespace_system_sharp_1_1_sys_d_o_m.html#af42b902eef7452e162a95b646eeea911ab4777b408acf603e260974d5d8e9e930">SystemSharp.SysDOM.Algebraic</a></div><div class="ttdoc">An algebraic quantity, i.e. a conceptually continuous number. </div></div>
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